A pharmaceutical company has developed a new medication to clear lung fluid buil

Question

A pharmaceutical company has developed a new medication to clear lung fluid build up in individuals with the flu. The company is planning a medical trial to determine, the average length of time between administering the medication and the removal of all fluid from the lungs. In the medical trial, n individuals who have gone to their primary care physician with flu like symptoms and who have fluid build up in their lungs will be given the new medication. The time, in hours, until each patient has no fluid in their lungs will be recorded. The company knows from previous experience that the population standard deviation will be no larger than std= 27 (hours). What is the minimum sample size that will guarantee that a 95% confidence interval for the mean (mew) will be less than 10 hours wide?

The answer is 113.
I just need to see the work to understand

Explanation / Answer

given sd= 27

mean = 10

n= ?

c.i of 95 = 1.96

Necessary Sample Size = (Z-score)² * StdDev*(1-StdDev) / (margin of error)²

Margin of error = Critical value x Standard deviation of the statistic

= 1.96*27=52.92

= 1.96^2*27(1-27) / 52.8^2

=3.8416( 702) / 2787.84

= 113.05

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